A smaller upper bound for the list injective chromatic number of planar graphs

An injective vertex coloring of a graph G is a coloring where no two vertices that share a common neighbor are assigned the same color. If for any list L of permissible colors with size k assigned to the vertices V ( G ) of a graph G , there exists an injective coloring phi in which phi ( v ) E L ( v ) for each vertex v E V ( G ), then G is said to be injectively k-choosable. The notation chi l i ( G ) represents the minimum value of k such that a graph G is injectively k-choosable. In this article, for any maximum degree O , we demonstrate that chi l i ( G ) <= O + 4 if G is a planar graph with girth g >= 5 and without intersecting 5-cycles.